Closed geodesics in simply connected Riemannian spaces of negative curvature
It is known that if a Riemannian variety of negative sectional curvature is homeomorphic to the 2-dimensional plane then there is no closed geodesic on this variety. Examples are known of Riemannian varieties of negative sectional curvature which are homeomorphic to \(\mathbb R^n\), \(n>2\), and have closed geodesics. In the article under review, the author obtains Riemannian varieties with sectional curvature \(\leq -1\) which are diffeomorphic to \(\mathbb R^n\) and have closed geodesics.
scientific article; zbMATH DE number 1564019